Doubly ionized helium ions are projected with a speed of 10 km s ⁻¹ perpendicular to a uniform magnetic field of magnitude 1.0 T . Calculate the radius of the circle in which an ion circulates.

Step-by-step solution

The mass of a doubly ionized helium ion (alpha particle) is m = 4 1.66 10⁻²⁷ kg = 6.64 10⁻²⁷ kg . The charge of the ion is q = 2e = 2 1.6 10⁻¹⁹ C = 3.2 10⁻¹⁹ C . The velocity of the ion is v = 10 km s ⁻¹ = 10^4 m s ⁻¹ and the uniform magnetic field is B = 1.0 T . The radius of the circular path is given by r = mv qB . Substituting the values: r = 6.64 10⁻²⁷ 10^4 3.2 10⁻¹⁹ 1.0 r = 6.64 3.2 10⁻⁴ m r 2.075 10⁻⁴ m 2.1 10⁻⁴ m